Mathematics High School

## Answers

**Answer 1**

If the point (0.42, y) is a **point** on the **unit** circle and 0 < y < 1, we can use the equation of the unit circle, which is x² + y² = 1.

**Substituting** the given x-coordinate, we have:

(0.42)² + y² = 1

0.1764 + y² = 1

y² = 1 - 0.1764

y² ≈ 0.8236

To find the value of y, we take the **square** **root** of both sides:

y ≈ √(0.8236)

Calculating the **approximate** value:

y ≈ 0.907

Therefore, the value of y, to the nearest hundredth, is approximately 0.91.

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## Related Questions

5) An alpha particle moves through a magnetic field along the parabolic path y = x2 – 4. Determine the closest that the particle comes to the origin.

### Answers

The closest **distance **that the alpha particle comes to the origin is √6 units, which occurs at x = ±√2 on the **parabolic **path y = [tex]x^{2}[/tex] - 4.

To find the **minimum **distance, we can use the concept of calculus. The distance between two points (x, y) and (0, 0) is given by the formula √(x^2 + y^2). Substituting the equation of the **parabolic path**, we have the distance function d(x) = √(x^2 + (x^2 - 4)^2).

To find the minimum, we take the derivative of the distance function, set it equal to zero, and solve for x. Then we substitute the obtained **value **of x back into the distance function to find the minimum distance.

By solving the **equation**, we find that the **closest **distance occurs at x = ±√2. Substituting this value into the distance function, we obtain the minimum distance of √6.

Therefore, the closest distance that the **alpha **particle comes to the origin is √6 units.

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(1 point) Find the derivative of 9(x) = 962 ** 52 u +3 -du u? + 3 g'(x) = HINT: 5 52 u +3 -du = 8. u? +3 u +3 u2 + 3 -dut u +3 du & u2 + 3

### Answers

The **derivative** of [tex]\(9(x) = 96^{2^{52u+3}}\)[/tex] is g'(x) = 0 which is calculated using the chain rule of differentiation.

In mathematics, the **derivative** shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus.

To find the derivative of [tex]\(g(x) = 9(x) = 96^{2^{52u+3}}\)[/tex], we need to use the chain rule.

Rewrite 9(x) using exponential notation: [tex]\(9(x) = 96^{2^{52u+3}}\)[/tex].

Take the natural **logarithm** of both sides to simplify the expression:

[tex]\(\ln(9(x)) = \ln(96^{2^{52u+3}})\)[/tex].

Apply the power rule of logarithms to bring down the exponent:

[tex]\(\ln(9(x)) = (2^{52u+3}) \ln(96)\)[/tex].

Differentiate both sides of the equation with respect to x using the chain rule:

[tex]\(\frac{d}{dx}(\ln(9(x))) = \frac{d}{dx}((2^{52u+3}) \ln(96))\)[/tex].

Apply the chain rule to differentiate ln(9(x)) with respect to x:

[tex]\(\frac{1}{9(x)} \cdot \frac{d}{dx}(9(x)) = (2^{52u+3}) \cdot \frac{d}{dx}(\ln(96))\).[/tex]

Simplify and solve for [tex]\(\frac{d}{dx}(9(x))\)[/tex]:

[tex]\(\frac{1}{9(x)} \cdot \frac{d}{dx}(9(x)) = (2^{52u+3}) \cdot 0\).[/tex]

Since [tex]\(\frac{d}{dx}(\ln(96)) = 0\)[/tex], we have:

[tex]\(\frac{1}{9(x)} \cdot \frac{d}{dx}(9(x)) = 0\)[/tex].

Multiply both sides by 9(x) to isolate [tex]\(\frac{d}{dx}(9(x))\)[/tex]:

[tex]\(\frac{d}{dx}(9(x)) = 0\)[/tex].

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You want to have $293,000.00 when you retire 28 years for an annuity. How much money should be deposited at the end of monthly in an investment plan that pays 4.4% compounded monthly, so you will have the $293,000.00 in 28 years?

### Answers

If you want to have $293,000 in **28 years**, you would need to put $267.72** **into an **investment plan** that pays 4.4% compounded monthly.

To solve this problem

We can use the formula for the **future value** :

[tex]FV = PMT * (1 + r/n)^n * nt[/tex]

Where

FV = Future ValuePMT = Paymentr = Interest Raten = Number of Compounding Periods per Yeart = Number of Years

In this case, FV = $293,000.00, PMT = ?, r = 0.044/12 = 0.00367, n = 12, and t = 28.

Solving for PMT, we get:

[tex]PMT = FV / (1 + r/n)^n * nt = $293,000.00 / (1 + 0.00367)^1^2 * 12 * 28 = $267.72[/tex]

Therefore, If you want to have $293,000 in **28 years**, you would need to put $267.72** **into an **investment plan** that pays 4.4% compounded monthly.

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Cuando te subes a una rueda de la fortuna, tus pies están a 1 pie del suelo. En el punto más alto del viaje, tus pies están a 99 pies del suelo. El viaje tarda 30 segundos en completar una revolución completa. Escribe una ecuación trigonométrica para tu altura sobre el suelo a los t segundos después de que comience el viaje. Encuentra en qué dos momentos dentro de un ciclo te encuentras exactamente a 90 pies del suelo

### Answers

**Podemos utilizar** la función arcoseno para encontrar los valores del ángulo (t) en los que se cumple la ecuación. Sin embargo, ten en cuenta que puede haber múltiples soluciones dentro de un ciclo. Por lo tanto, debemos encontrar los valores del ángulo que se encuentran en el intervalo [0, 2π] y** **satisfacen la ecuación.

t1 = (30/2π) arcsin(89/99)

t2 = π - (30/2π) arcsin(89/99)

Para escribir la ecuación **trigonométrica **que describe tu altura sobre el suelo en función del tiempo, podemos utilizar una función seno. La función seno tiene un periodo de 2π, lo que significa que se repite cada 2π unidades de tiempo.

Dado que el viaje tarda 30 **segundos** en completar una revolución completa, el periodo de la función seno será 30 segundos. Además, necesitamos considerar el desplazamiento vertical de la función seno, que en este caso es 1 pie.

Entonces, la ecuación que describe tu altura sobre el suelo a los t segundos después de que comienza el viaje es:

h(t) = 99 sin((2π/30) t) + 1

Para encontrar los dos momentos dentro de un ciclo en los que te encuentras exactamente a 90 pies del suelo, debemos resolver la ecuación:

99 sin((2π/30) t) + 1 = 90

Restamos 1 a ambos lados de la ecuación:

99 sin((2π/30) t) = 89

Luego, despejamos el ángulo:

sin((2π/30) t) = 89/99

Finalmente, **podemos **utilizar la función arcoseno para encontrar los valores del ángulo (t) en los que se cumple la ecuación. Sin embargo, ten en cuenta que puede haber múltiples soluciones dentro de un ciclo. Por lo tanto, debemos encontrar los valores del ángulo que se encuentran en el intervalo [0, 2π] y** satisfacen** la ecuación.

t1 = (30/2π) arcsin(89/99)

t2 = π - (30/2π) arcsin(89/99)

Los momentos dentro de un ciclo en los que te encuentras exactamente a 90 pies del suelo son t1 y t2,** **donde t1 y t2 están en el intervalo [0, 30].

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Let (n) be the number of positive divisors of n. Let (n) be the number of positive divisors of n which have remainders 1 when divided by 3. Find all possible integral values of the fraction 7(0m T(10n TI (10n)

### Answers

The possible **integral **values of the fraction 7(0m T(10n) TI (10n) are of the form 0m/100^k, where k is a **non**-**negative integer**, and m is any integer.

The expression given is 7((0m)/(T(10n)T(10n))).

Let's first focus on finding the possible values of (n).

Since the number of **divisors **of n is being denoted by (n), (1) will have only 1 divisor. Hence, (1) = 1.

For a prime number p, only 1 and p will be its **divisors**. Hence, (p) = 2.

If a number is in the form of p^k, where p is **prime**, the divisors will be 1, p, p^2, ..., p^k. Hence, (p^k) = k+1.

Using this, we can conclude that if n is of the form p^k, then (n) = k+1.

Now, let's focus on finding the **possible values **of (n) which have remainders 1 when divided by 3. This means that the divisors of n are of the form 3k + 1.

Let's consider a number of the form p^k, where p is a prime number of the form 3k + 1. The divisors of p^k will be of the form 3m + 1. Hence, (p^k) = k+1 will be a possible value of (n) which has remainders 1 when divided by 3.

So, we can write (n) = k+1, where k is a non-negative integer and p is a prime number of the form 3k + 1.

Now, let's simplify the given expression: 7((0m)/(T(10n)T(10n))) = 7(0m/((T(10n))^2))

We can now use the fact that the number of positive divisors of a number n is (n) to write the expression as: 7(0m/((T(10))^2(n))^2)

Substituting (n) = k+1, we get:

7(0m/((T(10))^2(k+1))^2)

= 7(0m/((100)^(k+1)))

= 7/((100)^(k+1)) * 0m

Since 7 and 100 are both **constants**, the possible values of the given expression are of the form 0m/100^k, where k is a non-negative integer.

Therefore, the possible **integral values **of the **fraction **7(0m T(10n) TI (10n) are of the form 0m/100^k, where k is a non-negative integer, and m is any integer.

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MATHHHHHHH HELLLLLLOPPPPPPPPPPO

### Answers

The required **equation **of the **directrix **is y = 11.

For a parabola in standard form, y = a(x - h)^2 + k, the focus is located at the point (h, k + 1/(4a)) and the **directrix **is given by the **equation **y = k - 1/(4a).

Comparing the given equation, y = -1/20 (x - 3)^2 + 6, to the **standard form**, we have h = 3, k = 6, and a = -1/20.

So, the focus is located at the point (3, 6 + 1/(4*(-1/20))) = (3, 1).

To find the equation of the directrix, we can use the formula y = k - 1/(4a) with the values we have:

y = 6 - 1/(4*(-1/20)) = 6 + 5 = 11

Therefore, the **equation **of the **directrix **is y = 11.

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Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents. (McGee, Williams, Howden-Chapman, Martin & Kawachi, 2006). In representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents scores on this questionnaire form a normal distribution with a mean of ?= 50and a standard deviation of ?=15. the sample group-participation adolescents had an average of M=53.8.

A) Does the sample provide enough evidence to conclude that self-esteem scores for those adolescents are significantly different from those of the general population? Use the two tailed test with a= .05

B)Comput cohens d to measure the size of the difference.

C) write a sentance describing the outcome of the hypothesis test and the measure of the effect size as it would appear in a research report.

### Answers

A) Yes, the **sample** provides enough evidence to conclude that self - esteem scores for these **adolescents** are significantly different from those of the general **population**.

B) The size of the **difference** measure is 0.22

C)The effect of those **activities** is small.

The information available from the question:

General population **mean** (null): [tex]\mu[/tex] = 50

Population **standard deviation** : σ =15

Sample mean : (x bar) = n53.8

Sample size n = 100

Level of **significance**: [tex]\alpha[/tex] = 0.05

(A) Yes, the sample provides enough evidence to conclude that self - esteem scores for these **adolescents** are significantly different from those of the general population. This was determined by conducting a one- sample **t - test:**

The hypotheses are:

[tex]H_0:\mu=50\\\\H_\alpha :\mu\neq 50[/tex]

Obtain the value of the standard error:

[tex]SE=\frac{s}{\sqrt{n} }[/tex]

[tex]SE =\frac{15}{\sqrt{100} }[/tex]

SE = 15/10

SE = 1.5

Apply the value for the **standard error **to the formula for the t- test statistic:

[tex]z=\frac{\mu_1-\mu_0}{SE}\\ \\z= \frac{53.8-50}{1.5}\\ \\z=\frac{3.8}{1.5}\\ \\z=2.5333[/tex]

To determine if our test statistic is significant, we must obtain a critical value for comparison. To do so, consult a table for the **z - distribution **associated with an alpha level of 0.05 for a two - sided test. this should give you a value of 1.96

P(Z< -1.96) + P(Z > 1.96) = 0.05

As our test statistic was more extreme than the critical value, we can confidently reject the** null hypothesis.**

B)To calculate Cohens d, apply the following formula for a one sample test:

[tex]d=\frac{\mu_1-\mu_0}{s}[/tex]

[tex]d=\frac{53.3-50}{15} \\\\d=0.22[/tex]

The resulting value fo**r Cohens d** indicates a small effect size.

C) Significant differences were found between the mean of the sample and the **mean** in the **population**, allowing us to reject the null hypotheses. Thus, childhood participation in sports, cultural groups, and youth groups does appears to be related to improved** self-esteem **for adolescents. With a Cohen's d value of 0.22, we conclude, however, that the effect of those activities is small.

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Plssss help with all,l of these answeres I will give brainliest and all my points plsssss

### Answers

**Answer: 1. 1/2 × b × h 2. 8 3. 25 4. 47.63 5. 240**

**Step-by-step explanation:**

Tom and Sally are at a carnival. At the carnival, participants earn tickets while playing different games. The tickets can then be turned in for prizes. Tom earns 5 tickets each time he plays the ring toss and 3 tickets each time he plays the fishing game. Sally earns 3 tickets for ring toss and 4 tickets for the fishing game. Tom needs to earn at least 15 tickets for the prize he wants. Sally needs to earn more than 12 tickets for the prize she wants.

a. Write a system of two linear inequalities to model the number of tickets Tom and Sally need to earn based on the number of times they play ring toss (x) and the number of times they play the fishing game (y).

b. What is the least number of times Sally needs to play only the ring toss in order to have enough tickets for the prize she wants?

c. Tom decides to play ring toss only 1 time. After that he will play the fishing game. What is the least amount of time Tom needs to play the fishing game in order to have enough tickets for the prize he wants?

### Answers

a. The system of two linear **inequalities **to model the number of tickets Tom and Sally need to earn based on the number of times they play ring toss (x) and the number of times they play the fishing game (y) is as follows:

For Tom: 5x + 3y ≥ 15 (Tom needs to earn at least 15 tickets)

For Sally: 3x + 4y > 12 (Sally needs to earn more than 12 tickets)

b. The least number of times Sally needs to play only the ring toss in order to have enough tickets for the prize she wants is 5 times.

c. The least amount of time Tom needs to play the fishing game in order to have enough tickets for the prize he wants is 4 times.

a. Let's define the **variables **x and y as the number of times Tom and Sally respectively play the ring toss game, and z and w as the number of times Tom and Sally respectively play the fishing game.

Based on the given information, we can write the following system of **linear **inequalities:

For Tom:

5x + 3z ≥ 15 (Tom needs to earn at least 15 tickets)

For Sally:

3y + 4w > 12 (Sally needs to earn more than 12 tickets)

b. To find the least number of times Sally needs to play only the ring toss, we can set the number of times she plays the fishing game (w) to zero and solve for y:

3y + 4(0) > 12

3y > 12

y > 4

Sally needs to play the ring toss more than 4 times in order to have enough **tickets **for the prize she wants.

c. Tom decides to play ring toss only 1 time.

After that, he will play the fishing game.

Let's find the least amount of time Tom needs to play the fishing game (z) in order to have enough tickets:

5(1) + 3z ≥ 15

5 + 3z ≥ 15

3z ≥ 10

z ≥ 10/3

Since the number of times Tom plays the fishing game cannot be fractional, we round up the result to the nearest whole number. Therefore, Tom needs to play the fishing game at least 4 times in order to have enough tickets for the prize he wants.

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The marginal profit of a company is modeled by; = dx √16x-5' units. Note at 10 units the profit is $260 a. Find the total profit function where x is the number of"

### Answers

The total profit **function **is:f(x) = (1/24) * (16x - 5)⁽³²⁾ + 260 - (1/24) * (155)⁽³²⁾.

The **marginal **profit of a company is modeled by; = dx √16x-5' units. Note at 10 units the profit is $260

to find the total profit function, we need to **integrate **the marginal profit function. the marginal profit function is given as f'(x) = √(16x - 5).integrating f'(x) will give us the total profit **function** f(x). let's proceed with the integration:

∫√(16x - 5) dxwe can simplify the integration by making a substitution. let's substitute u = 16x - 5. then, du/dx = 16, and dx = du/16.

substituting these values, we have:∫√u * (1/16) du

now, we can integrate √u with respect to u:(1/16) * ∫√u du = (1/16) * (2/3) * u⁽³²⁾ + c

simplifying further:(1/24) * u⁽³²⁾ + c

substituting back the original variable, we have:(1/24) * (16x - 5)⁽³²⁾ + c

this is the expression for the total profit function. however, to determine the constant of integration (c), we need additional **information**.given that at 10 units, the **profit** is $260, we can substitute this point into the total profit function and solve for c:

(1/24) * (16(10) - 5)⁽³²⁾ + c = 260(1/24) * (155)⁽³²⁾ + c = 260

now, we can solve for c:c = 260 - (1/24) * (155)⁽³²⁾

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compute the mean of the following population values 8,7,7,8,6

### Answers

The **mean**, also known as the **average**, is a measure of central tendency that represents the typical value in a set of data. To calculate the mean of a population, you need to sum up all the values and divide the sum by the total number of values.

For the population values 8, 7, 7, 8, and 6, you can add them together: 8 + 7 + 7 + 8 + 6 = 36. There are 5 values in the** population. **Next, you divide the **sum** by the total number of values: 36 / 5 = 7.2. This means that the mean of the population values 8, 7, 7, 8, and 6 is 7.2. In practical terms, the mean value of 7.2 represents the average of the population values. It indicates that if you were to choose a **random value** from the population, 7.2 would be a representative value. It can help provide a sense of the **central tendency **or typical value within the population.

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A survey of 850 people reported that 42% favored the re-election of the current governor. Find the margin of error.

### Answers

The **margin **of **error **is 88%

What is the margin of error for large samples?

Let that we have: Sample size n > 30

Sample standard deviation = s

Population standard deviation =[tex]\sigma[/tex]

Level of significance = [tex]\alpha[/tex]

Then the margin of **error**(MOE) is obtained as

Therefore **Population **standard deviation is;

Margin of Error = MOE = [tex]Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

Thus Population standard deviation is;

MOE = [tex]Z_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]

We are given that survey of 850 people reported that 42% favored the re-**election **of the current governor.

220 / 850 = 0.88

0.88 x 100 = 88

Therefore, The margin of error is 88%

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The line 5x-5y=2 intersects the curve x^2y-5x+y+2=0 at three points.

(a) find the coordinates of the points of intersection

(b) find the gradient of the curve at each of the points of intersection

### Answers

The gradients of the curve at the three points of **Intersection **are 5/17, -26/61, and -24/5, respectively.

The **coordinates **of the points of intersection between the line and the curve, we can substitute y = (5x - 2)/5 from the equation of the line into the equation of the curve, giving:

x^2((5x - 2)/5) - 5x + ((5x - 2)/5) + 2 = 0

Multiplying through by 5 to eliminate the **fraction**, we get:

x^2(5x - 2) - 25x + (5x - 2) + 10 = 0

Simplifying and rearranging, we get:

5x^3 - 24x + 8 = 0

This cubic equation can be solved using **numerical methods** or by using the Rational Root Theorem to find a rational root. One possible rational root is x = 2/5, which can be verified using polynomial long division. Dividing 5x^3 - 24x + 8 by (x - 2/5) gives:

5x^2 + 2x - 16

This quadratic factorizes as (5x - 8)(x + 2), so the other two roots are x = 8/5 and x = -2.

Substituting these values back into the equation of the line gives the corresponding y-coordinates:

- When x = 2/5, y = (5(2/5) - 2)/5 = 0

- When x = 8/5, y = (5(8/5) - 2)/5 = 2

- When x = -2, y = (5(-2) - 2)/5 = -2

Therefore, the three points of intersection are (2/5, 0), (8/5, 2), and (-2, -2).

To find the gradient of the curve at each of the points of intersection, we need to differentiate the equation of the curve with respect to x, giving:

x^2(dy/dx) + 2xy - 5 + dy/dx = 0

Simplifying and rearranging, we get:

dy/dx = (5 - x^2y)/(x^2 + 1)

Substituting the coordinates of each point of intersection, we get:

- At (2/5, 0): dy/dx = (5 - (2/5)^2(0))/((2/5)^2 + 1) = 5/17

- At (8/5, 2): dy/dx = (5 - (8/5)^2(2))/((8/5)^2 + 1) = -26/61

- At (-2, -2): dy/dx = (5 - (-2)^2(-2))/((-2)^2 + 1) = -24/5

Therefore, the gradients of the curve at the three points of intersection are 5/17, -26/61, and -24/5, respectively.

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A market research group wants to find out which of two brands of shoes causes blisters more often. They are considering three methods of gathering data:

Randomly choose 100 people. Ask them what shoes they typically wear and how often they tend to get blisters.

Randomly choose 50 people to wear on brand of shoes, and another 50 to wear the other brand. Compare the number of blisters that each group gets over the course of a month.

Find a group of 50 people that own the first brand of shoes, and another 50 people that own the second brand. Monitor how many blisters each group gets. Tell whether each method of gathering data is a survey, an observational study, or an experiment. Which option would give the most reliable results?

### Answers

The three **methods** of gathering data can be classified as follows:

Random survey of 100 people -** survey**

Random assignment of 50 people to each brand and comparing the number of blisters -** experiment**

Finding groups of 50 people for each brand and monitoring the number of blisters - **observational study**

The option that would give the most reliable results would be the randomized experiment (option 2), where the two groups of people are **randomly **assigned to wear one brand of shoes or the other, and then the number of blisters is compared between the two groups. This method allows for the control of other variables that could affect the occurrence of blisters, such as the activities or **environments **of the participants. The observational study (option 3) could be affected by other variables that are not controlled, such as the type of activities or **environments** the participants engage in. The survey method (option 1) relies on self-reported data, which may not always be** accurate** or representative of the entire population.

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x^3+14x^2+29x find the zeros

### Answers

Considering the definition of zeros of the quadratic function, the **zeros of the function** f(x) = x³ + 14x² + 29x are 0, -7-√80÷2 and -7+√80÷2.

Definition of zeros of a function

The points where a function crosses the axis of the independent term (x) represent the zeros of the function.

That is, the zeros represent the roots of the equation that is obtained by making f(x)=0.

In summary, the roots or zeros of a function are those values of x for which the** expression** is **equal to 0**. Graphically, the roots correspond to the abscissa of the** points** where the function **intersects the x-axis**.

In a **quadratic function** that has the form f(x)= ax² + bx + c the zeros or roots are **calculated by**:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

Zeros of f(x) = x³ + 14x² + 29x

The quadratic function is f(x) = x³ + 14x² + 29x

Since the **term "x"** is found in **all the terms**, it is extracted from the polynomial and is obtained:

f(x) = x(x² + 14x + 29), where one of the zeros of the function is zero.

Being for x² + 14x + 29:

a= 1

b=14

c=29

the **zeros or roots **are **calculated as**:

[tex]x1=\frac{-14+\sqrt{14^{2}-4x1x29 } }{2x1}[/tex]

[tex]x1=\frac{-14+\sqrt{80 } }{2}[/tex]

[tex]x1=-7+\frac{\sqrt{80 } }{2}[/tex]

and

[tex]x2=\frac{-14-\sqrt{14^{2}-4x1x29 } }{2x1}[/tex]

[tex]x2=\frac{-14-\sqrt{80 } }{2}[/tex]

[tex]x2=-7-\frac{\sqrt{80 } }{2}[/tex]

Finally, you get f(x) = x³ + 14x² + 29x= (x + 7 - √80÷2)(x + 7 + √80÷2) and the **zeros of the function** f(x) = 2x² + 16x – 9 are 0, -7-√80÷2 and -7+√80÷2.

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please answer all the questions! will give 5 star rating!

5. Evaluate the following limits : x2 +5x+4 x²1 (a) lim (b) lim *+-4x2–5x+6 ( 8pts) --- x2-3x-4 6. Find 2 numbers whose difference is 152 and whose product is a minimum. (Write out the solution) (

### Answers

5.(a) The value of lim (x² + 5x + 4)/(x² - 3x - 4) as x** approaches** 1 is -5/3.

(b) The **limit value** lim (-4x² - 5x + 6)/(x² + 5x + 4) as x approaches 1 is -3/10.

6. The solution is that any two numbers whose** difference **is 152 will have a minimum product of 152.

5 (a) To evaluate lim (x² + 5x + 4)/(x² - 3x - 4) as x approaches 1, we substitute x = 1 into the **expression**:

lim (1² + 5(1) + 4)/(1² - 3(1) - 4)

= lim (1 + 5 + 4)/(1 - 3 - 4)

= lim (10)/(-6)

= -5/3

5 (b) To evaluate lim (-4x² - 5x + 6)/(x² + 5x + 4) as x approaches 1, we substitute x = 1 into the expression:

lim (-4(1)² - 5(1) + 6)/(1² + 5(1) + 4)

= lim (-4 - 5 + 6)/(1 + 5 + 4)

= lim (-3)/(10)

= -3/10

6 To find two numbers whose difference is 152 and whose product is a minimum, we can set up an equation. Let's assume the two numbers are x and y, with x being the** larger number**.

The difference between x and y is given as x - y = 152.

To minimize the** product**, we need to maximize the difference between the two numbers. Since x is larger, we can express it in terms of y as x = y + 152.

Now, we substitute this value of x in terms of y into the** equation**:

(y + 152) - y = 152

Simplifying the equation gives us:

152 = 152

Since the equation is true, we can conclude that any two numbers that satisfy the condition x = y + 152 will have a minimum product of 152. The actual values of x and y will vary, as long as their difference is 152.

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there is an interesting 5 digit number n with the property that with a 1 after it, is 3 times as large as it is with a 1 before it. find n.

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The interesting 5-digit number is 60000. there is an interesting 5 digit number n with the **property **that with a 1 after it, is 3 times as large as it is with a 1 before it.

Let's call the 5-digit number n. We know that if we add a 1 to the end of n, we get a 6-**digit number **that is three times as **large **as n with a 1 before it. In other words, we have:

10n + 1 = 3(100n + 1)

Expanding the **right side **of the **equation**, we get:

10n + 1 = 300n + 3

Subtracting 10n from both sides, we get:

1 = 290n + 3

Subtracting 3 from both sides, we get:

-2 = 290n

Dividing both sides by 290, we get:

n = -1/145

However, we are looking for a 5-digit number, so this solution doesn't make sense. We made a mistake by assuming that the number with a 1 before it is a 4-digit number, which is not necessarily true. Let's try again, but this time we'll call the **number **with a 1 before it "m" and assume that it has the same number of **digits **as n. Then we have:

10m + n = 3(10n + 1)

Expanding the right side of the equation, we get:

10m + n = 30n + 3

Subtracting n from both sides, we get:

10m = 29n + 3

We know that n is a 5-digit number, so it must be between 10000 and 99999. We can use this to narrow down the possibilities for m. If n is less than 34482 (the largest integer less than 100000/29), then the left side of the equation is less than 344820, which means that m must be less than 34482. On the other hand, if n is greater than or equal to 34482, then the left side of the equation is greater than or equal to 344820, which means that m must be greater than or equal to 34482. Therefore, we have:

34482 ≤ m < n

Let's try some values of n within this range. If n = 40000, then we have:

10m + 40000 = 120001

Subtracting 40000 from both sides, we get:

10m = 80001

This doesn't work, since m is not an integer. Let's try n = 50000:

10m + 50000 = 150001

Subtracting 50000 from both sides, we get:

10m = 100001

This also doesn't work, since m is not an integer. Let's try n = 60000:

10m + 60000 = 180001

Subtracting 60000 from both sides, we get:

10m = 120001

This works! We have found that n = 60000 and m = 12000. Therefore, the interesting 5-digit number is 60000.

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elect the correct answer. Which statement is false? A. The inequality sign always opens up to the larger number. B. The greater number in an inequality is always above the other number on the vertical number line. C. The smaller number in an inequality is always located to the left of the other number on the horizontal number line. D. The inequality sign always opens up to the smaller number.

### Answers

The correct statement is that the **Inequality **sign always opens up to the larger number, not the smaller number.

The false statement is D. The inequality sign always opens up to the smaller number.

Inequality signs are used to compare two **quantities**, and they indicate the relationship between the two quantities. The symbol ">" means "greater than" and the symbol "<" means "less than". An inequality can also include the "equal to" **symbol**, which is represented by "≤" (less than or equal to) or "≥" (greater than or equal to).

When we plot inequalities on a number line, we can see the relationship between the two quantities. The **horizontal **number line represents the smaller quantity, and the vertical number line represents the larger quantity. The false statement in this question is that the inequality sign always opens up to the smaller number. In fact, the inequality sign opens up to the larger number.

For example, the inequality 3 < 5 means that 3 is less than 5. When we plot this on a number line, we put 3 to the left of 5 because 3 is smaller than 5. The inequality sign (<) opens up towards the larger number, which is 5.

Similarly, the inequality 7 > 2 means that 7 is greater than 2. When we plot this on a number line, we put 2 to the left of 7 because 2 is smaller than 7. The inequality sign (>) opens up towards the larger number, which is 7.Therefore, the correct statement is that the inequality sign always opens up to the larger number, not the smaller number.

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a software company uses two quality assurance (qa) checkers x and y to check an application for bugs. x misses 16% of the bugs and y misses 18%. assume that the qa checkers work independently.(a)what is the probability (as a %) that a randomly chosen bug will be missed by both qa checkers?let a be the event that a randomly chosen error is missed by proofreader x, and let b be the event that the error is missed by proofreader y. then, as percents, p(a)

### Answers

The **probability** that a randomly chosen bug will be missed by both QA checkers is 2.88%.

To find the probability that a** bug** is missed by both **QA checkers**, we need to calculate the probability of event A (bug missed by **proofreader** X) and event B (bug missed by proofreader Y) occurring simultaneously.

The probability of event A is given as 16%, which can be written as 0.16, and the probability of event B is given as 18%, or 0.18.

Since the checkers work independently, we can multiply the probabilities to find the probability of both events occurring: P(A and B) = P(A) × P(B) = 0.16 × 0.18 = 0.0288.

To express this probability as a **percentage**, we multiply by 100: 0.0288 × 100 = 2.88%.

Therefore, the probability that a randomly chosen bug will be missed by both QA checkers is 2.88%.

This probability represents the likelihood that a bug will go unnoticed by both QA checkers during the checking process.

It highlights the importance of having multiple QA checkers to increase the chances of identifying and fixing bugs in the software.

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if n is a positive integer and r is the remainder when 4 7n is divided by 3, what is the value of r ? (1) n 1 is divisible by 3. (2) n > 20

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This alone does not give us any information about the **remainder **when 4*7n is divided by 3. Therefore, statement (2) alone is not **sufficient **to determine the value of r.

We are given that n is a **positive** **integer **and r is the **remainder** when 4*7n is divided by 3. We need to find the value of r.

Statement (1) says that n+1 is **divisible **by 3. Let's see if this statement is sufficient to determine the value of r. Since n+1 is divisible by 3, we can write n+1 = 3k for some **integer **k. Then, 7n = 7(3k-1) = 21k - 7, and 47n = 28(3k-1). Now, we can use the fact that any integer can be written as one of three forms: 3k, 3k+1, or 3k+2. Since 28(3k-1) is a multiple of 3, its remainder when divided by 3 must be the same as the remainder when (3k-1) is divided by 3. When (3k-1) is divided by 3, the remainder is 2, so the remainder when 47n is divided by 3 is 2. Therefore, statement (1) alone is sufficient to determine the value of r.

Statement (2) says that n > 20. This alone does not give us any information about the remainder when 4*7n is divided by 3. Therefore, statement (2) alone is not sufficient to determine the value of r.

Since statement (1) alone is sufficient to determine the value of r, the answer is (A) statement (1) alone is sufficient, but statement (2) alone is not sufficient.

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da (i) +9 = cos t +861 - 7) subject to q(0) = 3 and g'(0) = -3 ( + + - q0 dt2 3

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The solution to the given **differential equation**, subject to the initial conditions q(0) = 3 and g'(0) = -3, is a = sin(t) + 845t + 3.

To solve the given **differential equation**:

da/dt + 9 = cos(t) + 861 - 7

with initial conditions q(0) = 3 and g'(0) = -3, proceed as follows:

Rewrite the equation in a more standard form by rearranging the terms:

da/dt = cos(t) + 861 - 7 - 9

Simplifying:

da/dt = cos(t) + 845

Integrate both sides of the equation with respect to t:

∫da = ∫(cos(t) + 845) dt

Integrating:

a = ∫cos(t) dt + ∫845 dt

a = sin(t) + 845t + C

Here, C is the constant of **integration**.

Apply the initial conditions to find the value of the constant C.

Given q(0) = 3, we substitute t = 0 and a = 3 into the equation:

3 = sin(0) + 845(0) + C

3 = 0 + 0 + C

C = 3

Substitute the value of C into the equation:

a = sin(t) + 845t + 3

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A video rental store keeps a list of their top 15 movie rentals each week next week the list includes six action for comedy three drama and two mystery the storm manager removes a copy of each of the 15 movies from the shelf then randomly select three of the 15 to show on display monitors in the store what is the probability that he selected two comedies in one action movie

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The **Probability **of selecting two comedies and one action movie in a specific order is 6/455.

The total **number **of ways to choose 3 movies from 15 is given by the combination formula:

C(15,3) = 15! / (3! * (15 - 3)!) = 455

To find the probability of selecting two comedies and one action movie, we need to calculate two probabilities separately: the probability of selecting two comedies and one action movie in any order, and the total number of ways to do so.

First, the probability of **selecting **two comedies and one action movie in any order can be calculated by multiplying the probabilities of each event happening.

There are 6 action movies and 3 comedies in the list of 15 movies.

So, the probability of selecting an action movie first is 6/15, or 2/5. The probability of selecting a second action movie is 5/14, since there are now 14 movies left and only 5 of them are action movies. The probability of selecting a comedy third is 3/13, since there are 3 comedies left and 13 movies left in total.

So, the probability of selecting two comedies and one action movie in any order is:

(6/15) * (5/14) * (3/13) = 1/91

Second, the total number of ways to select two comedies and one action movie in any order is given by the product of the number of ways to choose 2 comedies from 3 and 1 action movie from 6:

C(3,2) * C(6,1) = 3 * 6 = 18

So, the probability of selecting two comedies and one action movie in any order is 18/455.

Therefore, the probability of selecting two comedies and one action movie in a specific **order** (comedy, comedy, action) is:

(1/91) * (3!) = 6/455

Hence, the probability of selecting two comedies and one action movie in a specific order is 6/455.

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please help me solve this ive been stuck on this forever

(exponential growth and decay)

see attached photo

### Answers

The **population **10 years from now is about 1569.

We are given that;

Old Population= 1063

New population= 1273

Now,

We will plug these values into the formula and solve for r:

1273=1063e6r

Dividing both sides by 1063, we get,

10631273=e6r

Taking the **logarithm **of both sides, we get.

ln10631273=6r

Dividing both sides by 6, we get:

r=6ln10631273≈0.0348

Now that we have the **growth rate**, we will use it to find the population 10 years from now. We plug in t=10 and r=0.0348 into the formula and get:

P(10)=1063e0.0348×10≈1569.5

Therefore, by the given **exponential growth **the answer will be 1569.

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An experiment is conducted with a bag of marbles containing 5 red and 2 blue marbles. The results of a marble being drawn twice and replaced 100 times are shown in the table. Outcome Frequency Red, Red 19 Red, Blue 32 Blue, Blue 21 Blue, Red 28 Find P(no blue).

### Answers

The **probability** of getting no blue is 19/100.

Given that an **experiment** is conducted with a bag of marbles containing 5 red and 2 blue marbles.

The results of a marble being **drawn twice** and replaced 100 times are shown in the table.

**Outcome Frequency **= Red, Red 19 Red, Blue 32 Blue, Blue 21 Blue, Red 28

We need to determine the **probability** of getting no blue.

So, in every event there is a blue marble except the first event =

(red, red) = 19.

So, the probability of not getting a blue marble = 19/100

Therefore, **probability** of getting no blue is 19/100.

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how many times did lerena choose a golf ball from the bucket?

### Answers

**Answer:**

16 times and brainliest please!!!

**Step-by-step explanation:**

Let x represent the number of times Lorena chose a golf ball from the bucket. Since she chose a blue golf ball 9 times, the ratio of blue golf balls to total golf balls chosen is 9:x. Lorena predicts that if she chooses a golf ball from the bucket 160 times, 90 will be blue. So the ratio of blue golf balls to total golf balls chosen in this case is 90:160.

Since the ratios must be equal, we can write the equation 9/x = 90/160 and solve for x. Solving this equation, we find that x = 16.

So Lorena chose a golf ball from the bucket 16 times.

Find the curl of the vector field F =< 6ycos(x), 2xsin (y) >

### Answers

The curl of the **vector field** F =< 6ycos(x), 2xsin (y) > is given by (2sin(y) - 6cos(x)).

To find the curl of the vector field** **F =< 6ycos(x), 2xsin(y)>, we can use the formula for the curl of a vector field in two **dimensions**, which is given by:

curl(F) = (∂Q/∂x - ∂P/∂y)

In this case, we have P(x,y) = 6ycos(x) and Q(x,y) = 2xsin(y), so we need to compute the **partial derivatives** of these functions with respect to x and y.

∂P/∂y = 6cos(x)

∂Q/∂x = 2sin(y)

Therefore,

curl(F) = (∂Q/∂x - ∂P/∂y) = (2sin(y) - 6cos(x))

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6. What will the total amount of your $13, 075 if invested at 6.5% interest compounded

quarterly for 5 years?

### Answers

**Answer: It will be $18,048.99**

**Step-by-step explanation: Thats it**

A man gets a job with a salary of $39,200 a year. He is promised a $2,660 raise each subsequent year. During a 5-year period his total earnings are $ > Next Question K

### Answers

To calculate the man's total earnings during a 5-year period, we can use the arithmetic sequence formula to find the sum of an **arithmetic series**.

The first term, a, is $39,200, and the **common difference**, d, is $2,660.

The formula to find the sum of an arithmetic series is:

S_n = (n/2)(2a + (n-1)d)

where S_n is the sum of the first n terms, n is the number of **terms**, a is the **first term**, and d is the common difference.

Substituting the given values into the formula:

S_5 = (5/2)(2(39200) + (5-1)(2660))

= (5/2)(78400 + 4(2660))

= (5/2)(78400 + 10640)

= (5/2)(89040)

= 5 * 44520

= $222,600

Therefore, the man's total **earnings** during the 5-year period is $222,600.

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Three impedances are connected in parallel. Z -2-5j, Zn = 6 --, 23 - 2j. Find the equivalent admittance Y where 1 Y Z 22 23 1 Y- + + Express the admittance in both rectangular and polar forms. 0.23"

### Answers

Admittance in rectangular form: Y = (1/-2-5j) + (1/6) + (1/23-2j)

Admittance in** polar form**: |Y| = √(Re(Y)^2 + Im(Y)^2)

Resulting admittance: Y = |Y| ∠ θ = 0.23 ∠ 16.94°.

When three impedances are connected in **parallel**, the equivalent admittance Y can be found by summing the reciprocals of the individual impedances. Given the impedances Z1 = -2-5j, Z2 = 6, and Z3 = 23 - 2j, we can calculate the admittance Y as follows:

Y = 1/Z1 + 1/Z2 + 1/Z3

To express the admittance in **rectangular **form, we convert each impedance to its reciprocal and then add them:

Y = (1/-2-5j) + (1/6) + (1/23-2j)

To express the admittance in polar form, we convert the rectangular form to polar form by finding the **magnitude **(|Y|) and **angle **(θ) of Y:

|Y| = √(Re(Y)^2 + Im(Y)^2)

θ = arctan(Im(Y)/Re(Y))

The resulting admittance can be expressed as Y = |Y| ∠ θ = 0.23 ∠ 16.94°.

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Tracy manages an amusem*nt park.

She records the average amount of time in minutes that people wait in line to ride the roller coaster each day during one week.

She makes a line plot to show the wait times.

A line plot named

Which is an unreasonable conclusion about the wait times to ride the roller coaster?

### Answers

An **unreasonable conclusion** about the wait times to ride the roller coaster is : On one day, the lines were shorter than usual.

What will be unreasonable conclusion about the wait times

Tracy is said to make a line plot of average wait times to ride the **rollercoaster** for days in one week.

so the line plot is expected to have wait times for each day of the week** plotted **and we re told to examine a group of options to pick a conclusion that is unreasonable about the wait times to ride a roller coaster based on this line plot of average wait times per day for one week

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Complete question

Tracy manages an amusem*nt park. She records the average amount of time in minutes that people wait in line to ride the roller coaster each day during one week. She makes a line plot to show the wait times.

A.On one day, the lines were shorter than usual.

B. Riders can expect to wait about 10 minutes to ride the roller coaster.

C. There was an outlier to the average wait times.

D.There is no way to make a reasonable prediction of the wait time.